Using 3D-printed fracture networks to obtain porosity, permeability, and tracer response datasets

An in-depth understanding of flow through fractured media is vital to optimise engineering applications, including geothermal energy production, enhanced oil recovery, CO2 storage, and nuclear waste disposal. Advances in 3D-printing technologies have made it possible to generate 3D printed fracture networks with different fracture characteristics. By performing fluid flow experiments in the 3D-printed fractured networks, the impact of the fracture parameters, such as the density, orientation, aperture, dip, and azimuth, on the overall flow can be investigated. This data article contains a detailed description of the framework followed to design fractured networks with different fracture parameters and to create 3D-printed samples, including fracture networks. Furthermore, it contains the experimental protocols used to measure the porosity, permeability, and tracer responses of the 3D-printed samples. The generated datasets provided include geometry data describing the fracture networks, as well as porosity, permeability and tracer response data obtained from flow experiments conducted in the fracture networks.


Specifications
Earth and Planetary sciences, Engineering, Energy Specific subject area Fluid flow through fractured media Type of data CSV (Fracture information (center, radius, aperture, dip, azimuth)) STL (Fracture network 3D geometries) SCAD (Script for generation of fracture networks) Text (Tracer response) Xlsx (Permeability data, Porosity data) Table  Figure The three-dimensional STL files can be viewed using software such as Microsoft 3D viewer, Paraview, MeshLab, 3D Builder or Autodesk Fusion 360. Furthermore, the STL files can be uploaded directly to 3D printing software for 3D printing. The SCAD files can be used for generation of fracture network geometries using the OpenSCAD free software. How the data were acquired Generation of 3D fracture networks: Use of OpenSCAD software. Generation of 3D printed fracture network samples: Use of 3D-printer AGILISTA 3100 (KEYENCE CO.

Value of the Data
• Experimental data presented in this paper offer benchmark experimental datasets to validate theoretical/numerical models for fluid flow in fractured networks. • Understanding fluid flow in fractured media and building accurate numerical models is essential to optimise engineering applications, including contaminant transport, geothermal energy, enhanced oil recovery, CO 2 storage, and nuclear waste disposal. • Geometry data of fracture networks provided with this dataset can be used to generate 3D printing fracture network samples in order to perform experimental/numerical investigation of further fluid flow processes encountered in fractured media, such as thermal transport, reactive transport and multiphase flow. Furthermore, the code provided allows for altering the fractured networks used in this work.

Objective
The objective of this work is the development of benchmark experimental datasets which can be used to validate theoretical/numerical models describing fluid flow in fracture networks. 3D printing allows for the generation of three-dimensional complex fracture networks offering geometry control over the fracture network geometrical properties (e.g., fracture density, azimuth, density, aperture, and dip). Furthermore, 3D printing has been validated as a method of generating devices for fluid flow experiments [1] . By performing porosity and permeability measurements, in addition to tracer response experiments using the 3D-printed fracture network models, the impact of the fracture network properties on the overall flow can be investigated. Therefore, benchmark experimental datasets that could be used to validate theoretical/ numerical models can be obtained. The development and validation of the theoretical and numerical models describing fluid flow in fracture networks will allow optimization of engineering applications such as CO 2 storage, geothermal energy, and contaminant transport.

3D-Printed Fracture Network
The dataset contains geometry data of four 3D-printed fracture networks, including: (1) three-dimensional digital geometries of the fracture networks (.stl), (2) datasheets including fracture centres, radius, aperture, dip, and the azimuth of each fracture (.csv). Moreover, it contains (3) OpenScad scripts used for the generation of the geometries. The datasets and Open-SCAD scripts can be found in [2] . The 3D-printed network geometries can be seen in Fig. 1 .

Porosity Data
The porosities of the samples are listed in Table 1 . The parameters used for calculating porosity, such as density ρ (g.m −3 ) and viscosity μ (Pa.s) of the water, are listed in Table 2 .   Table 2 Parameters for the calculations. Parameter Value 8.90 × 10 −4 10 6 9.61 × 10 −4 0.1

Permeability Data
The relationship between pressure difference P (kPa) and flowrate Q (m 3 .sec −1 ) obtained from the flow experiments using the 3D-printed fracture network samples is presented in Fig. 2 . The parameters used for calculating permeability, such as cross-sectional area A (m 2 ) and length of the samples x (m) are also listed in Table 2 . The measured permeability values for the different 3D-printed fracture network samples are summarised in Table 3 . Moreover, the raw data can be found in the data repository (Permeability_data.xlsx).

Tracer Response Data
The temporal evolutions of Sodium ion (Na + ) concentration (ppm) measured at the outlet of each 3D-printed sample, obtained from the tracer response experiments, are shown in Fig. 3 . Furthermore, the raw data are provided in the data repository in the tracer response folder for each sample.

Generation of fracture networks
A detailed description of the fracture network generation can be found in [3] . The fracture networks were formed by disc-shaped fractures. The radii of the disc-shaped fractures were specified according to the power-law scaling with maximum and minimum radii. The fracture aperture was specified to be proportional to its radius based on linear elastic fracture mechanics [4] . The values of maximum and minimum radii were set to 15 mm and 1.6 mm, respectively. The ratio of fracture aperture to the length was set to 0.125, which was determined due to the limitation of the sample sizes and the precision of the 3D-printer. Fractures generated in this study were allowed to cross each other.
Fractures were generated until the fracture density reached the determined level with powerlaw fracture length distribution. The number of fractures in each sample N is given by (1) where C is the fracture density parameter, D is the fractal dimension, r min (m) and r max (m) are the specified radii of the smallest and largest fracture in the sample, respectively [ 5 , 6 ]. The locations and orientations of the fractures were randomly generated. The fracture network parameters for the four different samples generated can be seen in Table 4 . The fracture network geometries were printed using the inkjet 3D-printer AGILISTA 3100 (KEYENCE CO.). The AGILISTA 3100 uses two types of resin materials when performing the print, AR-M2 transparent UV-curable resin for the final geometry and AR-S1 for the support material, which is water soluble and is removed to reveal the final geometry by inserting the print into distilled water after printing [7] . The printer's resolution is 635 × 400 dpi, and the resolution at the X -axis is 15 μm.

Porosity Measurements
The experimental protocol for the porosity measurements of the 3D-printed samples can be seen in Fig. 4 . Firstly, the weight of the dried samples (i.e., dry weight) w dry was measured . Each sample was then placed in a beaker and filled with distilled water. The beaker was placed in a Desiccator (2-931-04 Forming Vacuum Desiccator (AS ONE Corp.)), which was connected to a rotary vane pump (RV Two Stage Rotary Vane Pump (Edwards Corp.)) and left to degas overnight. After the degassing process was completed, the sample was removed from the vacuum desiccator, the sides of the sample were wiped, and the weight of the saturated specimen with water (i.e., wet weight) w sat was measured. The porosity can be calculated as where V is the volume (m 3 ) of the sample and ρ water (kg.m −3 ) is the water density.

Permeability Measurements
The experimental apparatus for the permeability measurements can be seen in Fig. 5 . A container with distilled water was connected via 3mm ID tubing to a rotary vane pump (RV Two Stage Rotary Vane Pump (Edwards Corp.)), to a pressure regulator, and the inlet of the 3Dprinted sample. The sample outlet was connected via a 3mm ID tubing to a pressure regulator and a waste container. A flow test was then conducted by injecting distilled water at a constant flow rate Q (m 3 .sec −1 ) . For each sample, four flow experiments were conducted at four different flow rates, and the pressure difference P between the inlet and the outlet (Pa.s) was measured. Using the parameters from Table 2 , the permeability K (m 2 ) of the sample can then be calculated as [8] where P (Pa.s) is the pressure difference between inlet and outlet, μ (Pa.s) is the dynamic viscosity and x (m) is the length of the sample and A (m 2 ) is the cross-sectional area.

Tracer Response Measurements
The experimental apparatus for the tracer response measurements can be seen in Fig. 6 . A container with distilled water and a container with distilled water seeded with 90 0 0 ppm of Sodium ion (Na + ) tracer were connected via a 3mm ID tubing and a three-way valve, to a tubing pump (1-5916-01 Digital Quantitative Tubing Pump DSP -100S (AS ONE Corp.)). The pump was connected via a 3 mm ID tubing to the 3D-printed fracture network model. Firstly, the model was saturated with distilled water by injecting with a constant flow rate of Q = 10 −7 m 3 .sec −1 . After the fractured network was fully saturated with distilled water, the three-way valve was rotated to enable the injection of distilled water seeded with tracer inside the fracture network. The distilled water seeded with tracer was injected for 15 seconds, keeping the flow rate constant to Q = 10 −7 m 3 .sec −1 . After 15 seconds, the three-way valve was rotated again to enable distilled water injection. After two minutes of injection, which was the time it took for the tracer to reach the 3D-printed fracture network sample, we began to sample the fluid at the outlet every 10 seconds. The fluid samples were then analysed with a Sodium ion (Na + ) concentration sensor (LAQUAtwin Na-11 (Horiba Co.)). We used the time series of the Sodium ion (Na + ) concentration as tracer responses.

Ethics statements
The authors dully adhered to ELSEVIER 'Ethics in publishing' policy. No ethical issues are associated with this work.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Measurement of porosity, permeability, and tracer response using 3D-printed fracture networks (Original data) (OSF (Open Science Framework)).